WASHINGTON – President Barack Obama formally nominated Janet Yellen as the 15th chair of the Federal Reserve on Wednesday, ensuring that the powerful U.S. central bank will be led for the next four years by someone who shares the basic philosophy of the current chairman, Ben Bernanke.

The two agree that the central problem facing the U.S. economy is high unemployment; that the Fed can — indeed is obligated to — use its tools to try to fix that; and that monetary policy, whatever its limitations, is a powerful tool to try to make life better for millions of Americans.

While the philosophy atop the Fed will not be changing, what has changed in the eight years of Bernanke’s leadership are the demands of the job.

When Bernanke became chairman of the Fed on Feb. 1, 2006, this was the organization he led: It had $861 billion worth of securities on its balance sheet, almost all of it in simple Treasury bonds.

The Fed’s most recent policy statement was a simple 110 words long. The chairman never took on-the-record questions from the media. The Fed regulated banks, but that job was considered a backwater within the organization. The idea of the Fed bailing out an investment bank or an insurance company was downright preposterous. The unemployment rate was 4.7 percent.

When Yellen takes over on Feb. 1 (barring unexpected problems during her Senate confirmation hearing), she will probably inherit an organization more like this: A $4 trillion balance sheet stuffed with all manner of financial exotica, from mortgage-backed securities to portfolios acquired as part of the 2008 bailouts. Policy statements are now north of 700 words, explaining not just the Fed’s policy stance but what the central bank expects to do far into the future. Yellen will be expected to continue the practice of quarterly news conferences, or maybe even to turn them into an every-meeting, eight-times-a-year affair. And the organization she will run has the power to regulate any financial company, bank or otherwise, that endangers stability. The unemployment rate is 7.3 percent.

To lead the Fed or any major central bank has always been an extremely difficult job. To be a great central banker, a person must be an excellent economist, diplomat, politician, communicator, administrator and regulator — a mix of skills almost no one on Earth possesses. Indeed, Yellen comes closer to having the full mix you want in a Fed chief than Bernanke or his predecessor, Alan Greenspan; she has more extensive experience as a central banker than the two of them had combined before they were chairmen.

But because the Fed that Yellen inherits is even more complicated than those led by Bernanke and Greenspan, so too will be her challenges.

What unpredictable ripple effects is the multitrillion-dollar Fed balance sheet having for the global economy? What is the interplay between the Fed’s low interest rate policies and excessive risk-taking in different corners of the financial world? How do you apply the lessons of the crisis to regulate banks and other institutions more effectively? Does the very transparency that Bernanke has spent his chairmanship pushing create problems of its own?

Yellen has made her greatest mark as a thinker about employment and monetary policy. But when she becomes the chair, it will be her problem to come up with answers to this full gamut of questions.

In her comments Wednesday at the White House ceremony announcing her appointment, Yellen began by emphasizing the human impact of the recession, and the obligations of the Fed to help deal with it.

“The mandate of the Federal Reserve is to serve all the American people,” Yellen said. “And too many Americans still can’t find a job and worry how they’ll pay their bills and provide for their families. The Federal Reserve can help if it does its job effectively. We can help ensure that everyone has the opportunity to work hard and build a better life.”

Yellen is as accomplished as anybody on Earth in grappling with the questions of how the Fed might do exactly that — and that’s why the president appointed her. But her ultimate success will come not just from helping put America back to work, but also from mastering the broad complexities of what is, now more than ever, a nearly impossible job.